Modern Taylor Series Method in Numerical Integration

• Autorzy: Jan Chaloupka , Gabriela Necasová , Petr Veigend , Jirí Kunovský , Václav Šátek
• Języki publikacji: EN

Abstrakty

EN

The paper deals with extremely exact, stable, and fast numerical solutions of systems of differential equations. It also involves solutions of problems that can be reduced to solving a system of differential equations. The approach is based on an original mathematical method, which uses the Taylor series method for solving differential equations in a non-traditional way. Even though this method is not much preferred in the literature, experimental calculations have verified that the accuracy and stability of the Taylor series method exceed the currently used algorithms for numerically solving differential equations. The Modern Taylor Series Method (MTSM) is based on a recurrent calculation of the Taylor series terms for each time interval. Thus, the complicated calculation of higher order derivatives (much criticised in the literature) need not be performed but rather the value of each Taylor series term is numerically calculated. An important part of the method is an automatic integration order setting, i.e. using as many Taylor series terms as the defined accuracy requires. The aim of our research is to propose the extremely exact, stable, and fast numerical solver for modelling technical initial value problems that offers wide applications in many engineering areas including modelling of electrical circuits, mechanics of rigid bodies, control loop feedback (controllers), etc. (original abstract)

Słowa kluczowe

EN

Task scheduling theory; Differential equations; Mathematics

PL

Teoria szeregowania zadań; Równania różniczkowe; Matematyka

• Czasopismo: Systems Supporting Production Engineering
• Rocznik: 2017
• Numer: 6(4) Cross-Border Exchange of Experience in Production Engineering Using Principles of Mathematics
• Strony: 263--273

Twórcy

autor

Jan Chaloupka

• Brno University of Technology, Brno, Czech Republic

autor

Gabriela Necasová

• Brno University of Technology, Brno, Czech Republic

autor

Petr Veigend

• Brno University of Technology, Brno, Czech Republic

autor

Jirí Kunovský

• Brno University of Technology, Brno, Czech Republic

autor

Václav Šátek

• Brno University of Technology, Brno, Czech Republic

Bibliografia

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